Contents Preface ix PART I. Problems in Analysis An improvement of the Osserman constant for the bass note of a drum RODRIGO BANUELOS AND TOM CARROLL 3 Heat content asymptotics for some open sets with a fractal boundary M. VAN DEN BERG 11 On self-attracting random walks ERWIN BOLTHAUSEN AND UWE SCHMOCK 23 Positivity default for martingales and harmonic functions JEAN BROSSARD 45 Optimal switching between two Brownian motions R. CAIROLI AND ROBERT C. DALANG 53 Nonnegative solutions for semilinear elliptic equations with bound- ary conditions—a probabilistic approach Z. Q. CHEN, R. J. WILLIAMS, AND Z. ZHAO 65 Simulated annealing and fastest cooling rates for some 1-dim spin glass models TZUU-SHUH CHIANG AND YUNSHONG CHOW 83 Averaging stochastically perturbed Hamiltonian systems THOMAS G. KURTZ AND FEDERICO MARCHETTI 93 The interpretation and solution of ordinary differential equations driven by rough signals TERRY J. LYONS 115 Time-reversal of the noisy Wiener-Hopf factorisation L. C G. ROGERS 129 Some aspects of Brownian motion in a Poissonian potential ALAIN-SOL SZNITMAN 137
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