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  • 1.
    Aurzada, Frank
    et al.
    Technical University of Darmstadt, Germany .
    Dereich, Steffen
    University of Münster, Germany .
    Lifshits, Mikhail
    Linköping University, Department of Mathematics, Mathematical Statistics . Linköping University, The Institute of Technology. St. Petersburg State University, Russia.
    Persistence probabilities for a Bridge of an integrated simple random walk2014In: Probability and Mathematical Statistics, ISSN 0208-4147, Vol. 34, no 1, p. 1-22Article in journal (Refereed)
    Abstract [en]

    We prove that an integrated simple random walk, where random walk and integrated random walk are conditioned to return to zero, has asymptotic probability n(-1/2) to stay positive. This question is motivated by random polymer models and proves a conjecture by Caravenna and Deuschel.

  • 2.
    Liu, Zhenxia
    et al.
    Linköping University, Department of Mathematics, Mathematical Statistics . Linköping University, Faculty of Science & Engineering.
    Yang, Xiangfeng
    Linköping University, Department of Mathematics, Mathematical Statistics . Linköping University, Faculty of Science & Engineering.
    ON THE LONGEST RUNS IN MARKOV CHAINS2018In: Probability and Mathematical Statistics, ISSN 0208-4147, Vol. 38, no 2, p. 407-428Article in journal (Refereed)
    Abstract [en]

    In the first n steps of a two-state (success and failure) Markov chain, the longest success run L(n) has been attracting considerable attention due to its various applications. In this paper, we study L(n) in terms of its two closely connected properties: moment generating function and large deviations. This study generalizes several existing results in the literature, and also finds an application in statistical inference. Our method on the moment generating function is based on a global estimate of the cumulative distribution function of L(n) proposed in this paper, and the proofs of the large deviations include the Gartner-Ellis theorem and the moment generating function.

  • 3.
    Wahlberg, Patrik
    Univ Turin, Dipartimento Matemat, I-10123 Turin, TO, Italy.
    Regularization of kernels for estimation of the Wigner spectrum of Gaussian stochastic processes2010In: Probability and Mathematical Statistics, ISSN 0208-4147, Vol. 30, no 2, p. 369-381Article in journal (Refereed)
    Abstract [en]

    We study estimation of the Wigner time-frequency spectrum of Gaussian stochastic processes. Assuming the covariance belongs to the Feichtinger algebra, we construct an estimation kernel that gives a mean square error arbitrarily close to the infimum over kernels in the Feichtinger algebra.

  • 4.
    Wahlberg, Patrik
    et al.
    Univ Turin, Italy.
    Schreier, Peter
    Univ Gesamthsch Paderborn, Germany.
    On the instantaneous frequency of Gaussian stochastic processes2012In: Probability and Mathematical Statistics, ISSN 0208-4147, Vol. 32, no 1, p. 69-92Article in journal (Refereed)
    Abstract [en]

     We study the instantaneous frequency (IF) of continuous-time, complex-valued, zero-mean, proper, mean-square differentiable, non-stationaryGaussian stochastic processes. We compute the probability density function for the IF for fixed time, which generalizes a result known for wide-sense stationary processes to nonstationary processes. For a fixed point in time, the IF has either zero or infinite variance. For harmonizable processes, we obtain as a consequence the result that the mean of the IF, for fixed time, is the normalized first-order frequency moment of the Wigner spectrum.

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