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作者：NDUMU, MN
摘要：This paper deals with a heat kernel formula in a geodesic chart with some applications to the standard n-sphere. Our emphasis will be on the special case of the 3-sphere which exhibits some identities linking spherical harmonics and certain homogeneous polynomials harmonic on IR4. In particular, we will deduce an expression for P(x)(zeta > t) where zeta is the first (random) time that the bridge process in S3 hits the south pole. Another easy consequence will be a special case of the H.P. McKe...
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作者：ROGERS, LCG; WALSH, JB
作者单位：University of British Columbia
摘要：McGill showed that the intrinsic local time process LBAR (t, x), t greater-than-or-equal-to 0, x-epsilon-IR, of one-dimensional Brownian motion is, for fixed t > 0, a supermartingale in the space variable, and derived an expression for its Doob-Meyer decomposition. This expression referred to the derivative of some process which was not obviously differentiable. In this paper, we provide an independent proof of the result, by analysing the local time of Brownian motion on a family of decreasin...
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作者：IMKELLER, P
摘要：Let M be a martingale of pure jump type, i.e. the compensation of the process describing the total of the point jumps of M in the plane. M can be uniformly approximated by martingales of bounded variation jumping only on finitely many axial parallel lines. Using this fact we prove a change of variables formula in which for C4-functions f the process f(M) is described by integrals of f(k)(M), k = 1,2, with respect to stochastic integrators of the types expected: a martingale, two processes beha...
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作者：ALBEVERIO, S; ROCKNER, M
作者单位：University of Bonn
摘要：Using the theory of Dirichlet forms on topological vector spaces we construct solutions to stochastic differential equations in infinite dimensions of the type dX(t) = dW(t) + beta(X(t)) dt for possibly very singular drifts beta. Here (X(t))t greater-than-or-equal-to 0 takes values in some topological vector space E and (W(t))t greater-than-or-equal-to 0 is an E-valued Brownian motion. We give applications in detail to (infinite volume) quantum fields where beta is e.g. a renormalized power of...
