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Article
Noise Effect on the 2D Stochastic Burgers Equation
By comprehensive utilizing of the geometry structure of 2D Burgers equation and the stochastic noise, we find the decay properties of the solution to the stochastic 2D Burgers equation with Dirichlet boundary ...
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Article
Large deviation principle for multi-scale distribution-dependent stochastic differential equations driven by fractional Brownian motions
In this paper, we are concerned with multi-scale distribution-dependent stochastic differential equations driven by fractional Brownian motion (with Hurst index
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Article
Ergodicity of 3D Stochastic Burgers Equation
3D Burgers equation is an important model for turbulence. It is natural to expect the long-time behaviour for this hydrodynamics equation. However, there is no result about the long-time behaviour for this det...
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Article
Stochastic Averaging Principle for Two-Time-Scale SDEs with Distribution-Dependent Coefficients Driven by Fractional Brownian Motion
In this paper, we derive an averaging principle for a fast–slow system of stochastic differential equations (SDEs) involving distribution-dependent coefficients driven by both fractional Brownian motion (fBm) ...
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Article
A Strong Averaging Principle Rate for Two-Time-Scale Coupled Forward–Backward Stochastic Differential Equations Driven by Fractional Brownian Motion
This paper concerns the strong convergence rate of an averaging principle for two-time-scale coupled forward–backward stochastic differential equations (CFBSDEs, for short) driven by fractional Brownian motion...
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Article
On a Class of Distribution Dependent Stochastic Differential Equations Driven by Time-Changed Brownian Motions
In this paper, a class of distribution dependent stochastic differential equations driven by time-changed Brownians motion is studied. The existence and uniqueness theorem of strong solutions for the distribut...
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Article
Open AccessWell-Posedness for Stochastic Fractional Navier–Stokes Equation in the Critical Fourier–Besov Space
The well-posedness of stochastic Navier–Stokes equations with various noises is a hot topic in the area of stochastic partial differential equations. Recently, the consideration of stochastic Navier–Stokes equ...
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Article
Global Well-Posedness of Stochastic Nematic Liquid Crystals with Random Initial and Boundary Conditions Driven by Multiplicative Noise
The flow of nematic liquid crystals can be described by a highly nonlinear stochastic hydrodynamical model, thus is often influenced by random fluctuations, such as uncertainty in specifying initial conditions...
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Article
Stability of a Non-Lipschitz Stochastic Riemann-Liouville Type Fractional Differential Equation Driven by Lévy Noise
In this paper, stability of a non-Lipschitz stochastic Riemann-Liouville type fractional differential equation driven by Lévy noise is studied. Three types of stability, namely, stochastic stability, almost su...
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Article
Density Estimates for the Solutions of Backward Stochastic Differential Equations Driven by Gaussian Processes
The aim of this paper is twofold. Firstly, we derive upper and lower non-Gaussian bounds for the densities of the marginal laws of the solutions to backward stochastic differential equations (BSDEs) driven by ...
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Article
Least Squares Estimator for Path-Dependent McKean-Vlasov SDEs via Discrete-Time Observations
In this article, we are interested in least squares estimator for a class of path-dependent McKean-Vlasov stochastic differential equations (SDEs). More precisely, we investigate the consistency and asymptotic...
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Article
Open AccessMaximum principles for nonlocal parabolic Waldenfels operators
As a class of Lévy type Markov generators, nonlocal Waldenfels operators appear naturally in the context of investigating stochastic dynamics under Lévy fluctuations and constructing Markov processes with boun...
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Article
Open AccessOn drift parameter estimation for mean-reversion type stochastic differential equations with discrete observations
We are concerned with a parameter estimation for mean-reversion type stochastic differential equations (SDEs) driven by Brownian motion. The equations, involving a small dispersion parameter, are observed at d...
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Article
A comparison of two no-arbitrage conditions
We give a comparison of two no-arbitrage conditions for the fundamental theorem of asset pricing. The first condition is named as the no free lunch with vanishing risk condition and the second the no good deal...
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Article
Necessary and sufficient conditions for path-independence of Girsanov transformation for infinite-dimensional stochastic evolution equations
Based on a recent result on linking stochastic differential equations on ℝ d to (finite-dimensional) Burger-KPZ type nonlinear parabolic partial differential equations, we utili...
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Article
Stochastic control of SDEs associated with Lévy generators and application to financial optimization
This paper is concerned with the optimal control of jump type stochastic differential equations associated with (general) Lévy generators. The maximum principle is formulated for the solutions of the equations...
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Article
Stochastic differential equations with polar-decomposed Lévy measures and applications to stochastic optimization
This paper is concerned with the optimal control of jump-type stochastic differential equations associated with polar-decomposed Lévy measures with the feature of explicit construction on the jump term. The co...
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Article
On the Continuity of Pathwise Solutions to Langevin Equations in Infinite Dimensions
We fix a rich probability space (Ω,F,P). Let (H,‖⋅‖) be a separable Hilbert space and let μ be the canonical cylindrical Gaussian measure μ on H. Given any abstract Wiener space (H,B,μ) over H, and for every Hilb...
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Chapter
Nonstandard Construction of Stable Type Euclidean Random Field Measures
A nonstandard construction of stable type Euclidean random fields via hyperfinite flat integrals and stable white noise is given. Moreover, a brief account on an extension of Cutland’s flat integral formula fo...
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Chapter
Analytic and Probabilistic Aspects of Lévy Processes and Fields in Quantum Theory
A review of work on the description of generators and processes associated with stochastic (partial or pseudo-) differential equations driven by general white noises (including jump as well as diffusion parts)...
