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Mechanics of Random Motion
Small particles, such as electrons, perform a random zigzag motion (i.e., Brownian motion), which is unavoidable and intrinsic for small particles....
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Simulating Brownian Motion
Brownian motion and geometric Brownian motion are the most common models encountered in financial problems. In certain cases, it is possible to...
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A Generalized Stochastic Process: Fractional G-Brownian Motion
In this paper, a new concept for some stochastic process called fractional G -Brownian motion (fGBm) is developed. The fGBm can exhibit long-range...
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Nonparametric Estimation for Stochastic Differential Equations Driven by Mixed Fractional Brownian Motion with Random Effects
We discuss nonparametric estimation of the density of random effects in models governed by a stochastic differential equation driven by a mixed...
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On Some Distributional Properties of Subordinated Gaussian Random Fields
Motivated by the subordinated Brownian motion, we define a new class of (in general discontinuous) random fields on higher-dimensional parameter...
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The First Exit Time of Fractional Brownian Motion with a Drift from a Parabolic Domain
We study the first exit time of a fractional Brownian motion with a drift from a parabolic domain. Actually, we explore three different regimes. In...
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Four Finite Dimensional (FD) Surrogates for Continuous Random Processes
Numerical solutions of stochastic problems involve approximations of the random functions in their definitions by deterministic functions of time...
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An Interesting Class of Non-Kac Random Polynomials
As evident from classical results on random polynomials, it is difficult to derive the probability distribution of the number of real roots
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Fourier approach to goodness-of-fit tests for Gaussian random processes
A new goodness-of-fit (GoF) test is proposed and investigated for the Gaussianity of the observed functional data. The test statistic is the...
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Finding an NARE whose minimal nonnegative solution represents first passage quantities in the two-dimensional Brownian motion
The goal of this paper is to find a nonsymmetric algebraic Riccati equation(NARE) of which the minimal nonnegative solution can represent the Laplace...
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Hitting Time Problems of Sticky Brownian Motion and Their Applications in Optimal Stop** and Bond Pricing
This paper investigates the hitting time problems of sticky Brownian motion and their applications in optimal stop** and bond pricing. We study the...
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Bayesian Modeling in Engineering Seismology: Ground-Motion Models
The ground-motion model (GMM) is a key tool of the engineering seismologist. It predicts peak seismic ground-motion parameters given primary...
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A Collocation Method for Nonlinear Stochastic Differential Equations Driven by Fractional Brownian Motion and its Application to Mathematical Finance
The main aim of this article is to demonstrate the collocation method based on the barycentric rational interpolation function to solve nonlinear...
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Nonparametric Estimation of Trend for Stochastic Processes Driven by G-Brownian Motion with Small Noise
The present paper deals with the problem of nonparametric estimation of the trend for stochastic processes driven by G -Brownian motion with small...
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Random Assignment Versus Fixed Assignment in Multilevel Importance Splitting for Estimating Stochastic Reach Probabilities
This paper focuses on estimating reach probability of a closed unsafe set by a stochastic process. A well-developed approach is to make use of...
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Asymptotic inference for stochastic differential equations driven by fractional Brownian motion
We study a problem of parametric estimation for continuously observed stochastic processes involving fractional Brownian motion with Hurst index
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Random Apportionment: A Stochastic Solution to the Balinski-Young Impossibility
An apportionment paradox occurs when the rules for apportionment in a political system or distribution system produce results which seem to violate...
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Bayesian inference for fractional Oscillating Brownian motion
This paper deals with the problem of parameter estimation in a class of stochastic differential equations driven by a fractional Brownian motion with
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