Stochastic Equations Driven by a Cauchy Process
Vladimir P. Kurenok
Abstract
Using the method of Krylov’s estimates, we prove the existence of (weak) solutions of the one-dimensional stochastic equation dXt=b(Xt−)dZt+a(Xt)dt with arbitrary initial value x0∈ℝ and the driven symmetric Cauchy process Z. The bounded coefficient b is assumed to be of non-degenerate form and the drift a to satisfy the condition |a(x)|≤(1/2)|b(x)| for all x∈ℝ.
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Permanent link to this document: http://projecteuclid.org/euclid.imsc/1233152937
Digital Object Identifier: doi:10.1214/074921708000000327
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