Stochastic Integral Equations without Probability

Stochastic integral equations without probability

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Wilson wavelets for solving nonlinear stochastic integral equations

A new computational method based on Wilson wavelets is proposed for solving a class of nonlinear stochastic It^{o}-Volterra integral equations. To do this a new stochastic operational matrix of It^{o} integration for Wilson wavelets is obtained. Block pulse functions (BPFs) and collocation method are used to generate a process to forming this matrix. Using these basis functions and their operat...

Stochastic Integral Equations Associated with Stratonovich Curveline Integral

An explicit representation formula for a solution is given in Theorem 1, when g is a bounded smooth vector field. The case of a complete vector field g ∈ C1(Rn,Rn) is analyzed in Theorem 2, introducing adequate stopping times. The main support in writing a solution comes from the solution yλ(τ1, τ2) = G (F (τ1, τ2)) [λ], (τ1, τ2) ∈ R, λ ∈ R, satisfying a deterministic gradient system  ∂τ1yλ (...

Stochastic Volterra integral equations with a parameter

Abstract Cauchy problems and stochastic integral equations

Cauchy problems and stochastic integral equations Bachelor thesis, June 21, 2011 Thesis supervisor: dr. O. van Gaans Mathematisch Instituut, Universiteit Leiden