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Walsh’s theory of martingale measures in order to deal with stochastic partial differential equations that are second order in time, such as the wave equation and the beam equation,
Key words: Curvilinear integrals, H¨older continuity, rough paths, stochastic integrals, stochastic differential equations, fractional Brownian motion.. AMS 2000 Subject
Such neutral stochastic differential difference equations were introduced by Kolmanov- skii & Nosov [7], and the stability and asymptotic stability of the equations have also
In this paper we establish a stochastic formula to calculate the symbol of a class of Markov processes which we then apply to the solutions of certain stochastic differential
The natural question raised in [3] was then the following: is it possible to approximate equations like (1) in law by ordinary differential equations, thanks to a Wong-Zakai
Abstract: In this paper we give a solution for the one-dimensional reflected backward stochastic differential equation when the noise is driven by a Brownian motion and an
Since (3.10) is an ordinary integral equation, no stochastic integrals enter, so that if we choose ω so that t → Wt(ω) is continuous, the theory of (non-stochastic) integral
On the other hand, the study of these equations fits nicely into the the larger context of (stochastic) partial differential equations, in particular Hamilton-Jacobi, heat
