Results 21 to 30 of about 7,361 (311)
An Extension of the Stochastic Integral
The Annals of Probability, 1982 Two related extensions of the stochastic integral are discussed. These extensions allow the integrand to anticipate the Brownian motion, and arise in the study of linear stochastic integral equations. The development is based on the homogeneous chaos expansion of the integrand.
Berger, Marc A., Mizel, Victor J.
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A distributed procedure for computing stochastic expansions with Mathematica [PDF]
, 2013 The solution of a (stochastic) differential equation can be locally approximated by a (stochastic) expansion. If the vector field of the differential equation is a polynomial, the corresponding expansion is a linear combination of iterated integrals of ...
Ladroue, Christophe +2 more
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On extended stochastic integrals with respect to Lévy processes
Karpatsʹkì Matematičnì Publìkacìï, 2013 Let $L$ be a Levy process on $[0,+\infty)$. In particular cases, when $L$ is a Wiener or Poisson process, any square integrable random variable can be decomposed in a series of repeated stochastic integrals from nonrandom functions with respect to $L ...
N.A. Kachanovsky
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Stochastic Lie Group Integrators [PDF]
SIAM Journal on Scientific Computing, 2008 We present Lie group integrators for nonlinear stochastic differential equations with non-commutative vector fields whose solution evolves on a smooth finite dimensional manifold. Given a Lie group action that generates transport along the manifold, we pull back the stochastic flow on the manifold to the Lie group via the action, and subsequently pull ...
Simon J. A. Malham, Anke Wiese
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The Implementation of Milstein Scheme in Two-Dimensional SDEs Using the Fourier Method
Abstract and Applied Analysis, 2018 Multiple stochastic integrals of higher multiplicity cannot always be expressed in terms of simpler stochastic integrals, especially when the Wiener process is multidimensional. In this paper we describe how the Fourier series expansion of Wiener process
Yousef Alnafisah
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Exponential integrability of stochastic convolutions [PDF]
, 2003 Sucient conditions are found for stochastic convolution integrals driven by a Wiener process in a Hilbert space to belong to the Orlicz space expL2; standard exponential tail estimates follow from these results.
Seidler, Jan, Sobukawa, Takuya
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Open Mathematics, 2019 This paper aims to present a new pathwise approximation method, which gives approximate solutions of order 32$\begin{array}{} \displaystyle \frac{3}{2} \end{array}$ for stochastic differential equations (SDEs) driven by multidimensional Brownian motions.
Alhojilan Yazid
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A note on Kurzweil-Henstock's anticipating non-stochastic integral [PDF]
Mathematica BohemicaMotivated by the study of anticipating stochastic integrals using Kurzweil-Henstock approach, we use anticipating interval-point pairs (with the tag as the right-end point of the interval) in studying non-stochastic integral, which we call the Kurzweil ...
Yu Xin Ng, Tin Lam Toh
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Optimal Portfolios for Different Anticipating Integrals under Insider Information
Mathematics, 2020 We consider the non-adapted version of a simple problem of portfolio optimization in a financial market that results from the presence of insider information. We analyze it via anticipating stochastic calculus and compare the results obtained by means of
Carlos Escudero, Sandra Ranilla-Cortina
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On a Stochastic Integral Equation [PDF]
Proceedings of the Japan Academy, 1946 Not ...
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