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Notes on large deviations for branching processes indexed by a Poisson process
Consider a continuous-time process {ZN t } , where {Z n } is a Galton–Watson process with offspring mean m , and {N t } is a Poisson process independent of {Z
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Asymptotic Behaviors for Random Geometric Series
In this paper, we consider asymptotic behaviors for random geometric series. We first study the convergence rates in the central limit theorem, i.e.,...
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Asymptotic Upper Bound for the Peak-Effect in Linear Control Systems
AbstractThe large deviations of linear control system trajectories from the equilibrium position during the stabilization process, known as...
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Moderate Deviations for Stochastic Models of Two-Dimensional Second-Grade Fluids Driven by Lévy Noise
In this paper, we establish a moderate deviation principle for stochastic models of two-dimensional second-grade fluids driven by Lévy noise. We will...
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Large Deviations of the Range of the Planar Random Walk on the Scale of the Mean
We prove an upper large deviation bound on the scale of the mean for a symmetric random walk in the plane satisfying certain moment conditions. This...
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Rigorous Results in Space-Periodic Two-Dimensional Turbulence
We survey the recent advance in the rigorous qualitative theory of the 2d stochastic Navier–Stokes system that are relevant to the description of...
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The law of the iterated logarithm for two-dimensional stochastic Navier–Stokes equations
We implement the Azencott method to prove the moderate deviation principle for the two-dimensional incompressible stochastic Navier–Stokes equations...
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Moderate deviations for Euler-Maruyama approximation of Hull-White stochastic volatility model
We consider the Euler-Maruyama discretization of stochastic volatility model d S t = σ t S t d W t , d σ t = ω σ t d Z t , t ∈ [0, T ], which has been widely used in...
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Precise Asymptotics in Limit Theorems for a Supercritical Branching Process with Immigration in a Random Environment
Let ( Z n ) be a supercritical branching process with immigration in an independent and identically distributed random environment. Under necessary...
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Anscombe-type theorem and moderate deviations for trajectories of a compound renewal process
An Anscombe-type theorem for the large deviations principle for trajectories of a random process is proved. As a consequence, the moderate deviations...
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Product Measures
In this chapter we shall discuss the classical scheme of sums of independent random variables, which will allow us to sharpen many of the previous...
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Moderate deviations for estimators under exponentially stochastic differentiability conditions
We introduce two exponentially stochastic differentiability conditions to study moderate deviations for M-estimators. Under a generalized...
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Heat Transfer and Second Law Analysis of Ag-Water Nanoliquid in a Non-Uniformly Heated Porous Annulus
In majority of industrial and engineering applications, enhanced heat transfer with minimum entropy production is the major concern. With several...
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Moderate Deviations for a Stochastic Wave Equation in Dimension Three
In this paper, we prove a central limit theorem and establish a moderate deviation principle for a perturbed stochastic wave equation defined on
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On Probabilities of Moderate Deviations of Empirical Measures for Contiguous Distributions
The large deviation principle for moderate deviation probabilities of empirical measures for contiguous distributions is proved.
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Scientific School of Nonequilibrium Aeromechanics at St. Petersburg State University
AbstractThe review describes the creation and development of the scientific school of Sergei Vasilyevich Vallander at the Leningrad (now St....
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Risk and Potential: An Asset Allocation Framework with Applications to Robo-Advising
We propose a novel dynamic asset allocation framework based on a family of mean-variance-induced utility functions that alleviate the...
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What to offer if consumers do not want what they need? A simultaneous evaluation approach with an application to retirement savings products
Standard economic models of rational decision making provide information on how people should decide. In practice, human decisions are influenced by...
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Importance Sampling for the Empirical Measure of Weakly Interacting Diffusions
We construct an importance sampling method for computing statistics related to rare events for weakly interacting diffusions. Standard Monte Carlo...
